If you are looking for a place with no crowds, then Glacier is not it, we are already setting records this year and Going to the Sun is not even fully open yet, the last couple of years Glacier and Yellowstone has become very popular and setting records for visitors every single month they are open.
I have been watching the daily reports for both Apgar and Fish Creek and they are both full by noon everyday.
I was in town today(Kalispell) and there is already a ton of traffic, it won't get better after the 4th of July, so east or west, you are going to have to arrive at a campground early and possibly wait for someone to pull out, so you can snatch their spot as they vacate it.
I would actually recommend seeing if you can reserve a spot outside of the park, or see if you can get a reservation at Fish Creek for the days you want to visit, then just driving into the park during the day and finding a spot to park, so you can hike the various trails you want.
I have lived about 30 miles from the park for over 20 years now and it is busier now than it has ever been.
Good luck and have fun.